Deyverson missed two gilt-edged chances to earn three points for the hosts, with Atletico unable to create many openings in a toothless attacking display.
Atletico's problems with injuries and suspensions forced Simeone into an attacking team selection, but the Argentine said his side lacked focus.
"Alaves were superior, especially in intensity," Simeone said after Atletico drew their third successive match in all competitions.
"It was a bad game in general. [Nico] Gaitan had the clearest chance, but the goalkeeper reacted significantly and [Yannick] Carrasco played like the whole team, we must try to improve."
"We take a point, that is better than the game that could have been," Simeone said.
"It was not a good match in general but we will try to improve so that the next one is better. Alaves did not surprise me because it they play this way with all the teams."
Filipe Luis felt sloppy passing was one of the reasons Atletico struggled to work opportunities in front of goal.
"We have been overcome by Alaves," Filipe Luis said. "They have made a great game and we have not, we have failed passes, we have not found our game and they have overcome us in the aerial game and in the second plays.
"That is not the image that we would like to give and that is why we will work to improve.
"We wanted to win today, we were excited about this game and when you enter the field you win and play well you are always improving, you are gaining confidence.
"But we have already gone through worse times and surely our good football will return."